Servo system for a two-dimensional micro-electromechanical system (MEMS)-based scanner and method therefor

ABSTRACT

A servo control system for a micro-electromechanical systems (MEMS)-based motion control system (and method therefor), includes a motion generator having an inherent stiffness component.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention generally relates to a disk drive, and moreparticularly to a servo system for a two-dimensional MEMS-based scanner,and a method for use with the servo system.

[0003] 2. Description of the Related Art

[0004] A micro-electromechanical system (MEMS) can be utilized togenerate nanometer-scale motion. While providing nanometer-scale, yetprecise, positioning capability (e.g., 5 nm 1-sigma error), it isadvantageous to build a capability to span micrometer-scale areas (e.g.,100 μm square range) in the X-Y plane. The larger span range enhances ascanner's application potential. A key application of such a scanner isin the area of atomic force microscopy (AFM)-based storage applications,such as in a system disclosed in Vettiger and G. Binning, “The NanodriveProject,” Scientific American, pp. 47-53, January 2003, and PCTPublication No. WO 03/021127 A2.

[0005] In this system, a polymer media for recording information issupported by a scanner. Unlike a friction-free actuator system, such asthe one found in a disk drive actuator, a MEMS-based scanner isdominated by strong stiffness-producing flexural elements that provideX-Y freedom for movement. However, the presence of significant stiffnessin the actuator system is shown to produce steady position error withrespect to a ramp-reference trajectory in scan mode, and also suboptimalseek motion to a target track prior to a scan motion.

[0006] Thus, a new servo architecture is needed to overcome the effectof resistance generated by a system of flexural elements (i.e., that areintegral to a MEMS-based scanner) so that two-dimensional seek andtrack-following-scan performances are competitively achieved.

SUMMARY OF THE INVENTION

[0007] In view of the foregoing and other problems, drawbacks, anddisadvantages of the conventional methods and structures, an exemplarypurpose of the present invention is to provide a new servo architecture(and method therefor) which overcomes the effect of resistance generatedby a system of flexural elements (i.e., that are integral to aMEMS-based scanner) so that two-dimensional seek andtrack-following-scan performances are achieved.

[0008] In a first exemplary aspect of the present invention, a servocontrol system for a micro-electromechanical systems (NEMS)-based motioncontrol system, includes a motion generator having an inherent stiffnesscomponent.

[0009] In a second exemplary aspect of the present invention, a servocontrol system for a micro-electromechanical systems (NEMS)-based motioncontrol system, includes a scanner having an inherent stiffness, and afeedforward mechanism operatively coupled to the scanner forfeedforwarding a component for counterbalancing the stiffness of thescanner.

[0010] In a third exemplary aspect of the present invention, a servocontroller for controlling movement of a scanner, includes a servo unitfor generating a first-axis motion and a second-axis motion under atrack-follow-scan mode and a turn-around mode. A scan rate isprogrammable by choosing an appropriate slope for a ramp trajectory forthe servo unit when generating the first-axis motion.

[0011] In a fourth exemplary aspect of the present invention, a methodof storage-centric applications includes performing a two-dimensionalseek at a first speed and a first precision, and performing aone-dimensional scan at a second speed and a second precision. The firstspeed is higher than the second speed, and the first precision is lessthan the second precision.

[0012] In a fifth exemplary aspect of the present invention, a servocontrol system for a micro-electromechanical (MEMS)-based motion controlsystem, includes a proportional-integral-derivative (PID) controllerincluding a type-1 system. The controller has a steady position errordue to a ramp motion.

[0013] In a sixth exemplary aspect of the present invention, a method ofcontrolling a scanner in a microelectromechanical system (MEMS)-basedmotion control device, includes generating a velocity profile for eachX-seek, and managing a stiffness of the scanner.

[0014] With the unique and unobvious features of exemplary embodimentsof the invention, numerous exemplary advantages accrue. Indeed, theexemplary embodiments of the invention described herein develop a servostructure that augments a conventional control structure, including aproportional-integral-derivative (PID) type, so that the significantstiffness characteristics of a MEMS-based scanner are intelligentlyneutralized through an exemplary feed forward control method.

[0015] Thus, the invention provides several examples of a new servoarchitecture which overcomes the effect of resistance generated by asystem of flexural elements (i.e., that are integral to a MEMS-basedscanner) so that two-dimensional seek and track-following-scanperformances are achieved.

[0016] The present invention specifically addresses a plurality offunctions of a scanner developed for an AFM-based storage application,including a track-following-scan and a two-dimensional seek.

BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The foregoing and other purposes, aspects and advantages will bebetter understood from the following detailed description of a preferredembodiment of the invention with reference to the drawings, in which:

[0018]FIG. 1A illustrates elements of an AFM-based storage device 100with an X-Y scanner 110;

[0019]FIG. 1B illustrates details of a probe 120 for use with theAFM-based storage device 100;

[0020]FIGS. 2A-2C illustrate an optical position sensor 200 employed ina test configuration;

[0021]FIGS. 3A-3C illustrate seek and scan trajectories and theircomponents;

[0022]FIG. 4 illustrates scan mode reference trajectories;

[0023]FIG. 5 illustrates an architecture of a servo controller 500;

[0024]FIGS. 6A-6C illustrate a transfer function of the scanner alongone axis including Magnitude (FIG. 6A), Phase (FIG. 6B) and amass-spring-damper model (FIG. 6C);

[0025]FIGS. 7A-7B respectively illustrate a measured and a computed openloop transfer function (OLTF);

[0026]FIG. 8 illustrates a ramp reference (desired) trajectory for ascan mode and an actual (measured) trajectory;

[0027]FIGS. 9A-9C respectively illustrate an effect of plant parameterson position error for a ramp reference input;

[0028]FIG. 10 illustrates a feed forward configuration structure 1000 tominimize the impact of MEMS-stiffness on position error;

[0029]FIG. 11 illustrates a ramp reference trajectory and an actualresponse with stiffness compensation servo;

[0030]FIG. 12 illustrates a scanner displacement vs. current;

[0031]FIGS. 13A-13C illustrate two cases, with and without stiffnesscompensation servo, with position error shown in detail;

[0032]FIG. 14 illustrates an alternative configuration to reduce theimpact of stiffness (i.e., feedback mode);

[0033]FIGS. 15A-15C illustrate performance of a digital velocityestimator in scan mode;

[0034]FIGS. 16A-16E illustrate a single step seek to location-B followedby a PID scan;

[0035]FIGS. 17A-17E illustrate cascade steps to location-B followed by aPID scan;

[0036]FIGS. 18A-18D illustrate a velocity servo seek to Location-Bfollowed by a velocity servo scan with stiffness compensation; and

[0037]FIG. 19 illustrates a velocity profile and seek/track-follow-scannodes.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION

[0038] Referring now to the drawings, and more particularly to FIGS.1-19, there are shown preferred embodiments of the method and structuresaccording to the present invention.

Preferred Embodiment

[0039] Among several emerging non-volatile storage technologies,AFM-based storage promises to deliver more than 1 terabit/sq.inch arealdensity in a compact form factor device.

[0040] According to published information, 30-40 nm-sized bitindentations of similar pitch size have been made by a singlecantilever-tip assembly on a 50 nm thick polymethylmetacrylate (PMMA)layer (e.g., see P. Vettiger et. el., “The Millipede”-More than onethousand tips for future AFM data storage,“IBM J. Research andDevelopment, Vol. 44, No.3, pp.323-340, May 2000).

[0041] An integrated view of such a system 100 is shown in FIG. 1. Thesystem 100 includes an X-Y scanner platform 110, an X-Y stationarycantilever array chip 120 having a plurality of cantilever tiparray/probe assemblies (shown in greater detail in FIG. 1B), a storagemedia 130 on the X-Y scanner 110, an X-position sensor 140, a Y-positionsensor 145, an X-actuator 150, a Y-actuator 155, a stationary base 160,flexural supports 170 which provide freedom of motion, and amultiplex-driver 180.

[0042] As mentioned above, the details of the probe are as exemplarilyshown in FIG. 1B. The probe includes a resistive heater 121 coupledbetween two parallel beams (unreferenced) having a probe tip coupledthereto (unreferenced). The probe tip is stationary and the storagemedium to be read/written to includes pits 122 (representing informationin a manner well-known in the art) and is movable under the probe. It isnoted that the pits are formed in a polymer layer 123 formed on asubstrate 124 of the chip 125. The polymer under the tip (nanometerscale) is sensitive to the temperature radiation coming from the probetip. Thus, for writing to the storage medium (e.g., whenever a pit isdesired), a current is sent to the probe's heater element which heatsthe probe, and a pit (indentation) is formed on the polymer.

[0043] For reading, the probe is brought close to the polymer, andbecause of the presence of a pit (corresponding to a bit), the amount ofheat pulled out of the resistive element is less than the adjacent flatarea (e.g., the nonpit area). Thus, the change of resistance can bedetected, thereby representing the information therein. Hence, with sucha system, high areal density is achieved. Indeed, many thousands of suchprobes may be included in an array (e.g., 32×32), thereby allowingreading and writing simultaneously. Preferably, the probe is fixed andthe polymer/substrate is movable by means of the X-Y scanner system.

[0044] Each cantilever-tip/probe assembly 120 is associated with acorresponding data field. (Strategically selected data fields may beassigned to provide X-Y position information for a feedback servo loopas discussed below. Thus, high data rates are achieved by the paralleloperation of large, two-dimensional arrays (e.g., 32×32) ofcantilever-tip (referred to as tip-array) assemblies 120.

[0045] Time-multiplexed electronics control the read/write/erasefunctions needed in this storage device by activating the cantilever-tipsystem 120. In the system shown in FIGS. 1A-1C, the tip-array 120 isbuilt and assembled on the stationary chip 125, whereas the storagemedia (PMMA) 130 is deposited on the scanner 110 that is programmed tomove in an X-Y direction relative to the tip-array 120.

[0046] Sensing the position of the scanner 110 relative to the tip-array120 allows achieving reliable storage functions. Thermal expansion andmaterial creep over a long period of time can render a nanometer-scalestorage system useless, unless accurate position-sensing and servocontrol functions are embedded in the overall system design. In acommercialized version of the Millipede storage system, a positionsensor technology is embedded within the system.

[0047] To validate the present invention, an exemplary optical sensor isemployed that is shown in FIGS. 2A-2C. The sensor system 200 includes anedge sensor probe 210, and was custom built, for example, by MTIInstruments (e.g., see MTI Instruments Inc., Albany, N.Y., USA(www.MTIinstruments.com), employs a light beam transmitted by a lightsource 221 through an optical fiber 222 to shine a light at the movableedge of the MEMS.

[0048] The light beam through the optical fiber 222 is deflected by 90degrees using a miniature (e.g., 1 mm) prism structure including sets ofupper and lower prisms 220, 230, respectively.

[0049] In operation, the light beam from a light source 221 that passesover a moveable edge is captured by a prism of the second set of prisms230 (e.g., a lower prism), deflected by another 90 degrees, and istransmitted back to a receiving portion of the sensor electronics. Theamount of light received in proportion to the light sent forms the basisfor the voltage output of the edge sensor 210, and the voltage islinearly correlated to the location of the edge.

[0050] More specifically, the amount of light overlapping the prismindicates the position of the sensor. If the prism is completely blockedby the X-Y scanner platform, then no signal is returned, whereas if theprism is only 50 percent overlapping the X-Y scanner platform 110, thenonly 50 percent of the light is received, and a signal representing thesame can be output.

[0051] Having discussed a way to sense the scanner motion, it is notedthat read/write/erase (referred to as R/W) operations require twobroadly different position control capabilities as depicted in FIGS.3A-3C, including a 2-dimensional random seek and track-follow-scan.

[0052]FIGS. 3B and 3C define one of the several possible geometricallayouts for data recording where motion along a Cartesian coordinatesystem 300 is shown. The dots 310 in FIG. 3A signify the corner of theboundaries of each data field corresponding to each probe. Also shown isdata field 320.

[0053] As shown in FIG. 3C, a scanner with no control force applied toit (power off) (i.e., a relaxed mode) will initially rest at a “homeposition” denoted by Location-A in FIG. 3C.

[0054] Under active operation, for example, when access to a data block320 is required (for a read or a write), the scanner must be moved fromLocation-A to Location-B in two dimensions and preferably in minimumtime. The X-seek is nominally identical for all data blocks, whereas theY-seek is random.

[0055] Once Location-B is reached (e.g., through the random seek to atarget data block), the scanner must come to a stop, and change itsvelocity vector to move along a track in scan mode (with scan speed)towards Location-C, where the beginning of a data block is located. Forlong data records, the scanner must be able to reach the end of a trackalong the {+x} axis and then turn around (e.g., turn-around mode) andexecute a reverse direction scan along the {−x} axis, as shown in FIG.3B.

[0056] Thus, from location A-B, the scanner will move at seek speed(e.g., in two dimensions X, Y), and from location B-C the scanner willmove at scan speed (in one dimension X) to scan the track C.

[0057] It is noted that, as shown in FIG. 3B, it is desirable tominimize the “overshoot” (e.g., the margin area at location B of thedata block needed for the scanner to turn around) of the scanner duringits turnaround scan mode, thereby to increase the density of the chipand minimize the amount of wasted polymer space.

[0058] The scanner developed for this application has the freedom tomove along X and Y Cartesian coordinates independently. Thus, twodistinct position sensors and two feedback servo loops controlling twoelectromagnetic actuators, schematically shown in FIG. 1, are employedto develop the disclosed invention. It is noted that, in FIG. 1A, thefreedom to move along X-Y coordinates is in reality provided by acomplex system of flexures (details not shown), schematicallyrepresented by a single “spring” element for each degree of freedom ofmotion.

[0059] An industry-proven proportional-integral-derivative (PID)positioning servo system is a candidate controller for the MEMS scanner,designed for the storage application. A characteristic PID controllertransfer function, for example in analog form, is represented by thefollowing expression:

Controller (Output/Input)=(k _(P) +k _(D) s+k _(I) /s)   (1)

[0060] where gains k_(P), k_(D), and k_(I) are proportional, derivativeand integral gains, and ‘s’ is the Laplace transform operator. Theparameterization process to compute the gains is well known in thefield. A control system designer would use a dynamic model of thescanner and would derive the gain values to achieve an “optimum” design.

[0061] An integrated scanner/servo system is required to perform threecritical tasks.

[0062] First, it must move the scanner along the X and Y coordinates tothe vicinity of a target track (Location-B in FIG. 3C) in a minimum timeusing a velocity servo in a seek mode. To facilitate a robust andreliable seek to a target track, a desired velocity profile is typicallystored in memory and a velocity servo (in contrast to a position servo)is employed to reach the vicinity of a target track.

[0063] Next, the control system must position the scanner on the trackcenter line (TCL) of a target track using the Y-direction servo withminimum settle-out time using a position controller of the type shown inequation (1), with k_(I) normally set to 0.

[0064] Finally, the Y-servo system enters the track-follow mode with theY-servo having a proportional-integral-derivative type (PID) positioncontroller and the X-servo entering a scan mode desiring a fixed,predetermined scan velocity (by either using a position servo or avelocity servo). This operation is referred to as “track-follow-scanmode” to emphasize that the Y-servo is maintaining the storage mediaalong a TCL as the X-servo persistently maintains a predetermined scanvelocity. Both servos preferably maintain precision againstdisturbances, such as unknown hysteresis effects and vibration.

[0065] Scan Mode

[0066]FIG. 4 illustrates two reference trajectories to generate X and Ymotion under “track-follow-scan” and “turn-around modes”, where anexemplary X-scan length of 100 μm is to be achieved in 100 ms (1000μm/s), and the Y position is stepped by 40 nm at the end of a track. Thescan rate can be programmed by choosing an appropriate slope for theramp trajectory for the X-servo.

[0067] A complete servo architecture 500 to achieve this operation, aswell as the X-Y seek, is shown in FIG. 5. Architecture 500 includesX-servo 510 x and a Y-servo 510 y.

[0068] It is noted that, for completely decoupled dynamics of a scanneralong the X and Y coordinates, the servo system 500 can be selected tohave identical building blocks, but different controllers (position vs.velocity) may be switched in and out of the servo loop at various phasesof the scanner motion.

[0069] The position information is generated by the optical edge sensors(unreferenced in FIG. 5 and similar to those shown in FIGS. 2A-2C) andconverted to a stream of digital numbers (at 5 kHz in this example) byan analog-to-digital converter (ADC) 511 a, 511 y.

[0070] A digital controller for each axis includes a position controllerblock 512 x, 512 y, velocity estimator block 513 x, 513 y, velocitycontroller block 514 x, 514 y, reference trajectory block 515 x, 515 y,and a post filter bank 516 x, 516 y.

[0071] Under the supervision of a microprocessor, the functions providedby the blocks are activated appropriately. The computed control outputin digital form is sent to a digital-to-analog convertor (DAC) 517 x,517 y at a rate equal to, or different from, the input sampling rate.The analog signal generated by the DAC drives a current amplifier 518 x,518 y, which in turn respectively energizes the actuator 150, 155 of thescanner.

[0072] Scanner parameters, such as equivalent mass, spring stiffness,actuator force constants, etc., can be different for each X and Ymotion, and some parameters can drift with time and temperature. Theblock diagram of FIG. 5 can be further enhanced to include calibrationfunctions and other critical or auxiliary operations which are not thesubject of the present invention, but may be needed to make the servocontrol effective under different operating conditions.

[0073]FIGS. 6A-6B show the measured transfer function magnitude andphase of the scanner system corresponding to X-directional excitation,while the Y-direction actuator is held inactive (i.e., no Y-drivecurrent).

[0074] A second order equivalent model is shown in FIG. 6C, in which thedisplacement x corresponding to an input force F is resisted by a simplespring-mass-damper-like system below a frequency range of 2.5 kHz. Theequivalent spring stiffness k and mass m determine the fundamentalresonance frequency (200 Hz in this case). The damping constant cdetermines the quality factor Q of the fundamental resonance mode. Theexplicit presence of the stiffness term “k” is a key challenge inextracting optimum performance from a commercial product and is asubject of this invention. Beyond 2.5 kHz higher frequency resonancemodes start to contribute to motion along the X axis. In the exemplaryscanner, 3.0 kHz and 5.5 kHz modes are observable. Similar frequencycharacteristics along the Y-axis were observed in this scanner design bythe present inventors.

[0075] Thus, the simple schematic of FIG. 6C shows that the system willbehave very well as a simple spring mass system up to about 2.5 KHz.

[0076] To enhance nanoscale mechanics, the post filter bank 516 x, 516 y(shown in FIG. 5) can be configured to function as a notch or low-passfilter with relevant high frequency modes.

[0077] Thus, again FIGS. 6A-6C shows that the system of the inventioncan be viewed as a simple spring-mass system.

[0078]FIGS. 7A-7B show an open loop transfer function (OLTF)corresponding to a digital equivalent of a PID controller. Thetrack-follow servo for the Y-axis would use a PID digital controllerwith very similar properties to those shown in FIGS. 7A-7B. The computedand measured OLTF agree well since the MEMS system has a friction-freemotion capability (with mild hysteresis as discussed later).

[0079] However, the freedom from friction-induced performancedegradation is now replaced by an explicit “stiffness” term in the plant(i.e., scanner system) dynamics. As the MEMS-based scanner shouldachieve precise scan and optimum seek capability, it is important toevaluate its performance characteristics in the presence of a strongstiffness term.

[0080] Thus, using a reasonably well-known controller (e.g., PID-likecontroller), the flexure-based structure can be measured and modeled tofit to these curves. Thus, FIGS. 7A-7C show servo compensation beingemployed in addition to the basic spring mass system characteristicsshown in FIGS. 6A-6C.

[0081] If one wishes to perform a scan using the position controller,then FIG. 8 shows a comparison between a desired scan trajectory and ameasured scan trajectory under PID position control. Such a ramp(positive scan) in FIG. 8 is somewhat similar to what is shown in FIG.4, but is implemented using a position controller. The scan rate of (R=)500 μm/s produces a steady position error of 250 nm. Since the actualposition is known through direct measurement and the actual velocity isstill equal to the desired value, the position error with respect to thereference ramp may not be detrimental under certain Read/Writeconditions.

[0082] However, when the scanner trajectory is to be flexibly programmedusing an arbitrary reference trajectory, position error becomes animpediment, and it distorts the actual trajectory from the desired one.The position error “e” under a ramp trajectory represented by x=Rt,where “t” is the time, can be shown as:

e=R k _(Stiffness) /k _(I)   (2)

[0083] For a stiffness-free system, for example the case of abearing-supported mass, the stiffness contribution is minimum, and theerror term “e” is near zero.

[0084] For a MEMS with significant stiffness, equation (2) demonstratesthat the error grows linearly with stiffness. Especially in cases wherethe scan rate “R” is increased for certain error recovery or retryoperations during a R/W, the position error “e” can grow as well. Theerror term can nevertheless be reduced by increasing the integral gainterm “k_(I)”, but this method has limitations arising from control andstability considerations. Thus, an alternative method to minimize theerror “e” is desirable.

[0085] In characterizing structural properties of a control system, theOLTFs are classified as type-0, type-1, type-2 . . . systems (e.g., seeS. Gupta and L. Hasdorff, Fundamentals of Automatic Control, John Wiley& Sons, Inc., p.86, 1970.), where the type order is determined by thepower of the free standing denominator variable “s” of the OLTF. Thus,the term s¹ would indicate a Type-1 system.

[0086]FIGS. 9A-9C summarize three cases of a mass (m)-spring (k)-damper(c) system.

[0087] In the case of FIG. 9A, the plant is free to move along the xdirection under an excitation force F with no resistance. The planttransfer function (TF) (e.g., LaPlace transform) thus has a “s²” term inits denominator. Under a PD or a PID feedback control, the controlsystem becomes a type-2 or type-3 respectively. (Note that an integratorin a PID control introduces an extra term “s”, whereas a PD control willnot.) The steady state error due to ramp reference input for a system oftype-2 or higher can be proved to be null, as schematically shown forcases in FIGS. 9A-9C.

[0088] In the case of FIG. 9B, if there is only damping and nostiffness, for example the mass is immersed in a viscous liquid, thenthe new plant “s(m s+c)” has a single power for the free standing “s”.Under PD or PID control, the OLTF becomes either type-1 or type-2. Itcan be shown that, for a ramp input with a PD controller, there will bea steady-state position error, but with PID the error is null.

[0089] In the case of FIG. 9C which is more realistic and is the casefor a MEMS device, the OLTF with PD or PID will be either type-0 ortype-1. It will be illustrative to set up the OLTF for the PD and PIDcases as follows:

with a PD controller OLTF=(k _(P) +k _(D) s)/(ms ² +cs+k)   (3)

with PID controller OLTF=(k _(P) +k _(D) s+k _(I) /s)/(ms ² +cs+k)=(k_(D) s ² +k _(P) s+k _(I))/[s(ms ² +cs+k)]  (4)

[0090] It is observed that the power of the free standing “s” variablein the denominator of the OLTF is either 0 or 1, respectively. It can beshown that the corresponding error is either infinity or finite(equation 2). Experimental evidence, shown in FIG. 8, confirms that thesteady state position error is finite for a ramp reference input with aPID controller. With a simpler PD controller the error is unbounded andgrows with the amplitude of the ramp input.

[0091] The basic mechanism creating an error “e” is that, as rampreference displacement increases, the actual stiffness of the springcreates an increasing resistance to motion. Thus, a fixed gain term in aPD controller (equation (3)) can only produce a proportionallyincreasing drive force by growing the position error term with time atbest.

[0092] In the case of a PID controller, the integrator can produce acontinuously increasing drive force by means of a bias error in theposition represented by equation (2).

[0093] To minimize the error challenge, one approach is to introduce adouble integral in the controller. However, this method has stabilityimplications, since each integral introduces a 90-degree lag in thephase of the OLTF.

[0094] The present invention solves the stiffness-based resistance tomotion by providing a counter balancing force through electronic means.If the actual or desired position of the scanner is known, then anelectronically-generated force can be applied through the actuator toeliminate the resistance to motion.

[0095] When this form of counter balancing is augmented with aconventional PID controller, then the steady state position error for aramp reference input is minimized, while preserving the merits of afeedback control system.

[0096] Thus, now that it is known from FIGS. 9A-9C how the mechanismworks in producing the steady state position error, since the scannersystem has a stiffness which is measurable, and it is known what isdesired when a ramp motion is to be performed, such a burden need not beplaced solely on the servo controller.

[0097] Instead, FIG. 10 shows an exemplary structure 1000 of a feedforward configuration in which the anticipated stiffness term iscanceled by a feed forward element (e.g., through a stiffness termincluding either a k_(stiffness) unit 1020 for linear stiffness, or alook up table 1030 for complex stiffness).

[0098] Thus, in this exemplary embodiment the target term (e.g., thetarget reference) can be fed through the stiffness term digitally to theactuator as a current. Indeed, since it is known at each moment adesired position, if the corresponding spring force can be neutralized,then there is typically no restoring force which needs to be applied bythe controller itself. Thus, the exemplary approach of the presentinvention is to feed forward the stiffness term without waiting for thecontroller to build up.

[0099] That is, in the structure 1000 of FIG. 10, an input targetposition X-reference value (term) is provided to a node (e.g., a summingnode) 1010, a k_(stiffness) unit 1020 (for linear stiffness; case A inwhich k will be a constant term) and a table 1030 (for complexstiffness; case B in which k is a term having a complex, parabolic etc.type waveform). The node 1010 also receives a scanner position signalX-m from the scanner (having a position sensor) 110. The node 1010 takesthe difference between the target position X-reference and the measuredscanner position.

[0100] Based on the difference, the node unit 1010 outputs a positionerror signal (PES) to a servo controller 1040, which is also providedwith a reference velocity input 1050. An output U of the servocontroller is provided to a digital summing node 1060. The digitalsumming node 1060 also receives inputs U_(b) from k_(stiffness) unit1020 and table 1030, depending upon the linear stiffness or complexstiffness being present.

[0101] The node 1060 provides an output to an amplifier KA, which inturn amplifies (integrates) the signal from node 1060 and provides asignal U_(out) to the scanner. The scanner 110 in turn provides thescanner position X-m signal to the node 1010.

[0102] Thus, there are two possible approaches to generating the counterbalancing term.

[0103] In Case-A, the stiffness is known to be a linear ormathematically representable function. In this case, a compactcomputational representation from k_(stiffness) unit 1020 would besufficient to compute the required actuator current.

[0104] In Case-B, the resistance force is a complex function ofposition. In this case, the look-up table 1030 is constructed employinga calibration method in which the quasi-static current (mA) vs.displacement (μm) data is measured and stored therein.

[0105] When FIG. 10 is implemented, the results shown in FIG. 11 areobtained.

[0106] That is, FIG. 11 shows the positive effect of using the stiffnesscounterbalancing feed forward method during a ramp motion. Compared tothe case corresponding to FIG. 8, the position error component is almostunobservable. A linear approximation to the stiffness is used to computethe counterbalance force. The stiffness term is derived by performing aquasi-static calibration.

[0107] By injecting a steady current in steps of 5 mA from the neutralposition (Location-A) of the scanner and observing the correspondingequilibrium position of the scanner, the necessary stiffness term isderived. The result of the calibration is shown in FIG. 12.

[0108] On the scale of 20 μm displacement, the displacement plot appearsvery linear. However, the forward/return motion due toincreasing/decreasing current is not identical. The difference betweenthe forward position and the return position for the same current isplotted as the “delta,” with its scale on the right side of the plot ofFIG. 12. A difference of about 50 nm can be expected. Likewise, a finerscale calibration near the origin may yield a stiffness that isdifferent from the average stiffness. Further analysis is needed tochoose a method to accurately represent the stiffness term. It is notedthat any non-linearity in the actuator force generation capability isimplicitly included in the composite representation by the plot in FIG.12.

[0109] Thus, the inventors found that, by going from a forward directionand then going in the backward direction by increasing the current to 40mA and then decreasing the current from 40 mA, because siliconsubstrates have some inherent relaxation in stiffness, then thecorresponding position may not be exactly the same when the current goesback to the original 30 mA, for example. However, the difference willnot be substantial and will not be outrageously inaccurate. By the sametoken, it will be useful to use a feedback controller to manage thevariations, but the gross stiffness element is addressed by the system'sfeedforward scheme of the present invention.

[0110] The detailed position error characteristics, including thereference and actual trajectories for both cases (corresponding to FIGS.8 and 11), are shown in FIGS. 13A-13C. The position error has beenreduced from 250 nm to 50 nm for a nominal stiffness value. The positionerror component can be easily driven to near zero by updating thestiffness term as frequently as necessary.

[0111] The stiffness counterbalancing effect can also be achieved in afeedback mode in which the measured position is positively fed back, asshown in FIG. 14. Thus, FIG. 14 shows another way to achieve the sameresult as the system of FIG. 10. However, in the case of the system ofFIG. 14, the stiffness term of the scanner 110 is made to appear as 0(null) to the controller.

[0112] Hence, since a position sensor is disposed for providing anabsolute position (or a position with regard to a neutral position),such a stiffness term (which is positive) can be fed through a stiffnesselement 1420 (in a digital processor or the like) to a digital summingnode 1460 to counterbalance. Thus, in this exemplary embodiment, thescanner 110 plus the stiffness term (which is a positive equivalentfeedback force) will counterbalance the negative value of the scanneroutput, thereby resulting in a free (floating) system.

[0113] In this method, while making the plant appear like a systemwithout stiffness, the PID controller must be redesigned to account forthe modified plant characteristics. As noted above, the feedback methodrequires reliable position measurement through out its operation. Anoverestimate of the stiffness can also result in an unstable plant whenthe conventional control is not activated as it is in a positivefeedback configuration.

[0114] Furthermore, any noise in the position measurement couldtranslate into a spurious disturbance component, thus generating anundesirable positioning error. The feed-forward method, using thereference position signal, is thus preferable to the feedback method.

[0115] Velocity Estimator

[0116] Scan mode and seek mode operations require knowledge of thescanner velocity along each axis. Under a velocity servo mode, anestimate of the velocity is repeatedly used to generate the controlvalues. The position control servo exploits the velocity estimates toensure, for example, that the desired switching conditions from avelocity to a settle-out position servo are met at the end of a Y-seek.It is noted that the cost of embedding a velocity sensor, in addition toa position sensor, can be excessive and may usurp the electronic circuitresources. Since the scanner position is sampled at discrete timeinstants separated by a fixed duration (i.e., sampling period), a simpleestimate of scanner velocity is the arithmetic difference betweenadjacent position values. However, in practice the position-differencemethod becomes corrupted by the measurement noise, and newly developedstatistical estimation methods could be considered (e.g., see R. F.Stengel, Stochastic Optimal Control, John Wiley & Sons, Inc., Chapter 4,1986).

[0117] A state variable-based full state estimator (including thevelocity) is employed to obtain the estimates of the scanner along the Xand Y axes. The following variables are first defined:

[0118] n=Sampling instant;

[0119] U(n)=Actuator Current Driver input expressed in DAC Bits;

[0120] Y(n)=Actuator Position Sensor output expressed in ADC Bits;

[0121] V(n)=Actuator Velocity in ADC Bits/Sample;

[0122] X1(n)=Estimated Position in ADC Bits;

[0123] X2(n)=Estimated Velocity (=V(n)); and

[0124] X3(n)=Estimated Unknown force in DAC Bits.

[0125] By casting the scanner dynamics as a second order system with twostate components X1 and X2, and by augmenting the second order modelwith an additional state X3 representing the unmodeled portion of theforce (e.g., see M. Sri-Jayantha and R. Stengel, “Determination ofnonlinear aerodynamic coefficient using the Estimation-Before-ModelingMethod,” Journal of Aircraft, Vol. 25, no. 9, pp. 796-804, September1988) acting on the scanner, a state estimator of the following form canbe formulated:

X1(n)=A1*X1(n−1)+A2*X2(n−1)+A3*X3(n−1)+B1*U(n−1)+G1*Y(n)

X2(n)=A4*X1(n−1)+A5*X2(n−1)+A6*X3(n−1)+B2*U(n−1)+G2*Y(n)   (5)

X3(n)=A7*X1(n−1)+A8*X2(n−1)+A9*X3(n−1)+B3*U(n−1)+G3*Y(n)

[0126] where constants [A1 through A9], [B1 B2 B3] and [G1 G2 G3] aredetermined by the parameters of the scanner transfer function (TF) andthe desired filtering characteristics of the estimator. The filteringproperty is broadly governed by the characteristic roots of the dynamicsystem represented by equation (5) above.

[0127]FIGS. 15A-15C show the effect of the estimator characteristicsunder a scan mode (e.g., from location B to location C in FIG. 3C).These Figures show that a very sophisticated velocity estimator as anexemplary part of the entire implementation of the invention.

[0128]FIG. 15A corresponds to a ramp rate of 5000 nm/10 ms, which isalso equal to a scan rate of 100 nm/sample at a 5 kHz sampling rate.Thus, FIG. 15A shows the measured and estimated position.

[0129]FIG. 15B shows a position difference and an estimated velocity,employing matrix equation (5) with the characteristic root at a 1500 Hzradius. FIG. 15B shows the digital estimator to be very “fast”, meaningthat it does not filter very much. As shown, there are many sharp peaks(“wiggles”) in the waveform during the steady velocity, whereas if thereis a redesign of the filter to slow down or to add more filteringcharacteristics (e.g., to filter better) to the estimator, then theresults will be as shown in FIG. 15C in which the velocity is made“smoother”, and thus much better than that of FIG. 15B.

[0130] That is, FIG. 15C shows the same position difference plotcompared to a redesigned velocity estimator (e.g., Velocity Estimator 2)having a 1000 Hz characteristic root. It can be observed that theestimator has the capability to filter noise depending on the choice ofits characteristic root as a design parameter. An estimator with a 1000Hz characteristic root is used in the subsequent application to optimizeX-seek.

[0131] Thus, the velocity estimator can be designed optimally to havebetter filtering characteristics.

[0132] Seek Mode

[0133] The seek mode performance is considered for optimization. In thescanner servo, both X and Y directional seeks are required. The Y-seekhelps the scanner to move to a target track (e.g., Location-B in FIG.3C) with zero terminal velocity since the subsequent motion for a R/Wrequires the scanner to maintain the tip-array along the TCL with zeromean velocity across the Y-axis.

[0134] However, the X-seek demands innovative consideration. It not onlyneeds to optimize a seek criteria (such as minimum time or minimumovershoot into the margins of the storage media), it also has to producea reverse velocity equal to the scan rate along X before a R/W canbegin.

[0135] Progressively complex control methods can be devised to enhanceX-axis seek control. First, three methods will be described below toenhance X-axis seek control, and then some experimental results will beshown.

[0136] The three methods include:

[0137] Method-1). A long step input to Location-B from Location-A isfirst made using a PID-like position servo. Once the destination isreached and a terminal velocity of zero is attained, the PID-likeposition controller driven by a ramp-reference trajectory with feedforward stiffness compensation is used. Extra space along the X-axis isneeded to accommodate step input overshoot, as well as a “take-offrunway” to accelerate the scanner from rest position to the desired scanspeed;

[0138] Method-2). A cascade of short steps are generated untilLocation-B is reached, and the scan phase is initiated, as in the abovecase. In this case, the step input overshoot is decreased, but the seektime is likely to be increased; and

[0139] Method-3). A velocity servo is used to follow a referencevelocity trajectory all the way to Location-B where the direction ofmotion is changed under the same velocity servo and the scan mode isinitiated using the same velocity servo. In this approach, the time tomove from Location-A to a R/W ready condition is observed to be theleast. Moderate overshoot space is still required in cases in which thevelocity vector undergoes a 180-degree change of direction.

[0140]FIGS. 16A-16B correspond to Method-1. That is, a single step moveto region B is made, to move there fast with some overshoot and thenhesitate a while before following a ramp.

[0141] Method 1 does not take advantage of the k_(stiffness),feedforward to the k_(stiffness), knowledge of the system, etc., butdoes have feedforward during the scan. However, this feed forward isimmaterial to this case since it is focussed on moving from location Ato location B.

[0142] It can be seen that a 5 μm X-axis motion requires about 3 μmovershoot and 1 μm for the “take-off runway” needed for scan modeinitialization. Before reaching the desired scan velocity, total time isabout 11.5 ms.

[0143]FIGS. 16B-16D correspond to position (repeat of FIG. 16A),velocity and current commands, respectively.

[0144]FIG. 16E shows a two-dimensional representation (e.g., movement inX and Y) with no time scale displayed on it. It is noted that theY-scale is much finer (granular) than the X-scale. The seek operationbegins from rest Location-A and moves to a target track near Location-B,followed by a Y-track follow servo and X-scan servo (e.g., referred toas a “track-follow-scan”). The “border” region covered by Location-Bwhere the seek to track-follow-scan transition occurs is critical to theRIW performance, as well as an effective use of storage media. The scantracks are separated by a 200 nm track pitch in this exemplary test.

[0145] Thus, FIG. 16E shows movement from original location A (e.g., theoriginal rest position) to location B, overshoot at location B,turnaround, activate the scan and begin scanning to location C, stepdown, reverse scan across, step down, then perform a scan, etc.

[0146]FIGS. 17A-17E correspond to Method-2. This method recognizes thata single large step may be excessive. Thus, this method attempts tominimize overshoot, but at the expense of total time required which ismuch higher than that required in Method 1.

[0147] Hence, in Method-2, a cascade of mini-step moves reduces theovershoot to almost 0 μm with 1 μm still needed for the “take-offrunway”, but total time rises to 15 ms. More specifically, a pluralityof approximately 0.5 to 1.0-micron size steps leading to the targetposition of approximately −5000 nm in FIG. 17A. However, in theexemplary embodiment, the steps may be permitted to move to −6000 nm toget ready for the scan and to minimize the transient delay.

[0148]FIGS. 17B-17D correspond to position (repeat of FIG. 17A),velocity and current commands, respectively.

[0149]FIG. 17E shows the two-dimensional representation of the testresults similar to that of FIG. 16E. The extended scan along many tracksseparated by a 70-nm track pitch is demonstrated in this example. Thisconfiguration was studied before the stiffness counterbalance method wasdeveloped.

[0150] Without exploiting the knowledge of the scanner stiffness, thepresent inventors found that it was difficult to design a velocitycontroller (at a 5 kHz sampling rate) to encompass desirableseek-settling characteristics. The controller not only should accelerateand decelerate the scanner mass, but it also should build up acontinuously increasing and rapidly leveling (near Location-B) counterforce against the stiffness resistance. While the overshoot distance isminimized, the seek to scan time is lengthened to 15 ms. This is not acompetitive tradeoff between border margins for overshoot vs. seek-scantime.

[0151] Thus, Method-1 is faster (11.5 ms) to reach the scan mode, butrequires a large border area, whereas Method-2 uses less “real estate”(border or margin area) but is slower, requiring 15 ms (e.g., about 3.5ms more than Method-1) to activate the scan mode.

[0152]FIGS. 18A-18E correspond to Method-3, which was designed tooptimize the above-described methods (e.g., optimize both margin andtime). Continuous velocity servo for seek and scan requires only 3 msseek-scan time, and 0.5 μm border space for regaining the scan velocity.Method-3 produces the most competitive results in which both seek timeand border (or margin) length is minimized.

[0153] Optimizing the transition from seek to track-follow-scanoperations as accomplished by Method-3 uses two innovative steps.

[0154] A first step is the generation of a velocity profile for eachX-seek. The velocity profile that normally would terminate at nullvelocity when the target distance approaches zero should beconstructively modified to extend beyond zero as terminal velocity, andshould impart a reverse velocity equal to that of the desired scan rate,and continue to maintain the scan rate until the end of the track isreached. (At the end of a track, the turn-around occurs. This isachieved by a step move by a Y-position servo, while the X-scan servoproduces the same scan rate in the opposite direction.) A schematic ofthe velocity profile and modes of the X-Y controllers are shown in FIG.19.

[0155] A second optimizing step is that of managing the “stiffness”problem. Higher sampling rates facilitate easy design tradeoffs. Atsampling rates envisioned to be competitive, the seek controllers arefound to require augmentation. The anticipated force to keep the scannerat equilibrium near Location-B can be computed from the knowledge ofstiffness as discussed above.

[0156] Hence, to assist the acceleration (in -ve direction along the Xaxis) a step change in controller output equal to the equilibrium valueis generated. The velocity estimator is activated by this control outputin addition to the velocity servo output that attempts to follow thereference velocity profile.

[0157]FIGS. 18A-18B show the X-seek and scan performance for a 5 μummove with different vertical scales. Five seek and scan operations arerepeated to show the robustness of the access operation.

[0158]FIGS. 18A-18B show the time evolution of position from Location-Ato Location-B along the X axis (-ve).

[0159]FIG. 18C shows the estimated velocity. It is observed that thepeak velocity of 1250 nm/sample is achieved in 6 samples (1.2 ms),hardly enough for the controller to build up against the scanner'sstiffness.

[0160]FIG. 18D shows the stiffness feed-forward output alone (e.g., arelatively powerful output current), and the velocity controller outputwhen it is added to the stiffness feed forward output. The feedforwardstiffness term allows the controller to adjust its behavior to thetrajectory as exemplarily shown in FIG. 19. It is observed from thisplot that the servo controller output (without the stiffness term) ispositive for the first 3 samples, and negative for the next 7 samples inthis example. The net actuator current is almost always in onedirection, indicating that the deceleration is provided by the stiffnessof the scanner alone. The velocity controller cushions the decelerationlevel by the spring so that the transition to scan-mode is achieved inlimited samples. It has been demonstrated that a conservative seek timeof 10-15 ms can be reduced to 3 ms through the two innovative stepsdemonstrated in the present invention.

[0161] The stiffness feed forward component can be optimized further bymaking it more complex. By stepping the output level in conjunction withthe acceleration/deceleration/scan phases, the move time can be furtherreduced. This is a subject beyond the scope of the present invention.The switching criteria that will be universal for all seek lengths,especially when the X-Y dynamics are coupled, can be difficult toachieve and needs further effort.

[0162]FIG. 18E, similarly corresponding to Method-3, illustrates thetwo-dimensional seek performance of the system of Method-3.

[0163] Thus, Method-3 implements the velocity trajectory along with thestiffness feedforward, as shown in FIG. 18D. In an exemplary embodiment,Method-3 preferably employs the system of FIG. 10 using Case-A, and inwhich the servo controller 1040 is fed with the reference velocity 1050,whereas Methods 1 and 2 in exemplary embodiments preferably employX-position controller 512 (as opposed to the velocity controller).Obviously, other configurations are possible as would be known by one ofordinary skill in the art taking the present specification as a whole.

[0164] With the above-described unique and unobvious exemplaryembodiments of the present invention, a servo structure is developedthat augments a conventional control structure, including aproportional-integral-derivative (PID) type, so that the significantstiffness characteristics of a MEMS-based scanner are intelligentlyneutralized through an exemplary feed forward control method.Additionally, a feedback control method is described in which numerousadvantages accrue.

[0165] Thus, as described above, the invention provides several examplesof a new servo architecture which overcomes the effect of resistancegenerated by a system of flexural elements (i.e., that are integral to aMEMS-based scanner) so that two dimensional seek andtrack-following-scan performances are achieved.

[0166] Further, the present invention addresses a plurality of functionsof a scanner developed for a AFM-based storage application, including atrack-following-scan and a two-dimensional seek.

[0167] While the invention has been described in terms of severalpreferred embodiments, those skilled in the art will recognize that theinvention can be practiced with modification within the spirit and scopeof the appended claims.

[0168] Further, it is noted that, Applicant's intent is to encompassequivalents of all claim elements, even if amended later duringprosecution.

What is claimed is:
 1. A servo control system for amicro-electromechanical systems (MEMS)-based motion control system,comprising: a motion generator having an inherent stiffness component.2. The system of claim 1, further comprising: a feed-forward element forcanceling the inherent stiffness component.
 3. The system of claim 2,further comprising a node coupled to receive an input from saidfeed-forward element, wherein said feed-forward element comprises one ofa linear stiffness unit and a look-up table for storing therein complexstiffness, for generating a stiffness component, based on a targetposition first-axis reference signal, for being input to said node. 4.The system of claim 1, further comprising: a node coupled to said motiongenerator, and a stiffness term unit coupled between said motiongenerator and said node, wherein a target reference term is input viathe stiffness term unit digitally to the node as a current.
 5. Thesystem of claim 1, further comprising: a servo controller for receivinga position error signal based on a target position first-axis referencesignal, and a reference velocity, wherein the stiffness term is fedforward without waiting for the servo controller to build up.
 6. Thesystem of claim 1, further comprising: a node for receiving an inputtarget position first axis-reference value; a k_(stiffness) unit for alinear stiffness; and a look-up table for storing values representingcomplex stiffness, wherein said node further receives a motion generatorposition first axis-signal from the motion generator.
 7. The system ofclaim 6, further comprising: a servo controller coupled to an output ofsaid node, said node outputting a position error signal (PES) to saidservo controller, said servo controller further receiving a referencevelocity input; and a node for receiving an output from said servocontroller, and an output from one of said k_(stiffness) unit and saidlook-up table, based on a linearity of said stiffness.
 8. The system ofclaim 7, further comprising: an amplifier for receiving and amplifyingan output from said node, to provide an output to the motion generator.9. The system of claim 1, further comprising: a scanner including aposition sensor, a first-axis/second axis table, and said motiongenerator.
 10. The system of claim 8, wherein said motion generatorprovides an output position signal to said node.
 11. The system of claim1, further comprising: means for generating a counter balancing term tosaid inherent stiffness component.
 12. The system of claim 11, whereinsaid means for generating comprises a k_(stiffness) unit for a conditionwhen the stiffness is one of linear and a mathematically representablefunction.
 13. The system of claim 11, wherein said means for generatingcomprises: a look-up table for a condition when the stiffness comprisesa complex function of position.
 14. A servo control system for amicro-electromechanical systems (MEMS)-based motion control system,comprising: a scanner having inherent stiffness; and a feedforwardmechanism operatively coupled to said scanner for feedforwarding acomponent for counterbalancing the stiffness of said scanner.
 15. Thesystem of claim 14, wherein the stiffness of said scanner, whencounterbalanced by said feed forward component, minimizes a positionerror of said scanner due to a ramp motion.
 16. The system of claim 14,wherein a seek motion control is optimized by initiating a seek with acounterbalancing force that is expected at an end of the seek orbeginning of a scan position.
 17. The system of claim 16, wherein afirst-axis-velocity profile for the seek completes the seek motion witha desired scan speed.
 18. A servo controller for controlling movement ofa scanner, comprising: a servo unit for generating a first-axis motionand a second-axis motion under a track-follow-scan mode and aturn-around mode, wherein a scan rate is programmable by choosing anappropriate slope for a ramp trajectory for the servo unit whengenerating the first-axis motion.
 19. The servo controller according toclaim 18, wherein said servo unit comprises: a first servo for theX-axis and a second servo for the Y-axis.
 20. The servo controlleraccording to claim 19, wherein said first servo comprises: ananalog-to-digital (A/D) converter for receiving position informationsignals of said scanner, and converting said position informationsignals to digital values; a digital controller including: a positioncontroller for receiving an output from said A/D converter; a velocityestimator for receiving an output from said A/D converter; a velocitycontroller for receiving an output from said velocity estimator; areference trajectory for providing an input to said velocity controller;and a post filter bank for receiving an output from one of said velocitycontroller and said position controller, to provide a control signal; adigital-to-analog (D/A) converter for receiving said control signal andgenerating an analog signal; a current amplifier for receiving saidanalog signal; and an actuator for receiving an output from said currentamplifier to drive said scanner.
 21. A method of performingstorage-centric applications, comprising: performing a two-dimensionalseek at a first speed and at a first precision; and performing aone-dimensional scan at a second speed and at a second precision,wherein said first speed is higher than said second speed, and whereinsaid first precision is less than said second precision.
 22. The methodof claim 21, further comprising: optimizing a seek motion control byinitiating a seek with a counterbalancing force that is expected at anend of the seek or at a beginning of a scan position.
 23. The method ofclaim 22, wherein a first-axis-velocity profile for the seek iscompleted with a desired scan speed.
 24. The system of claim 1, furthercomprising a digital velocity estimator having a known bias allowing anestimate of velocity in a flexure system of the MEMS-based motioncontrol system.
 25. The system of claim 1, further comprising: afeedback element for canceling the inherent stiffness component.
 26. Thesystem of claim 25, wherein the inherent stiffness component iscounterbalanced such that a measured position is positively fed back.27. The system of claim 25, further comprising a scanner comprising themotion generator, and wherein the stiffness term of the scanner is madeto appear as null to a controller.
 28. The system of claim 25, furthercomprising a node for providing an input to said motion generator and astiffness element coupled to said node, wherein a term representing saidinherent stiffness component is fed through said stiffness element tosaid node to counterbalance the stiffness.
 29. The system of claim 20,wherein the velocity estimator is designed optimally to havepredetermined filtering characteristics.
 30. The system of claim 28,wherein said velocity estimator has a predetermined fast filteringcapability at a cost of allowing larger noise peaks occurring in awaveform during a steady velocity.
 31. The system of claim 28, whereinsaid velocity estimator has a predetermined slow filtering capabilitysuch that a waveform during a steady velocity is substantially uniform.32. A servo control system for a micro-electromechanical (MEMS)-basedmotion control system, comprising: a proportional-integral-derivative(PID) controller comprising a type-1 system, said controller having asteady position error due to a ramp motion.
 33. A method of controllinga scanner in a micro-electromechanical system (MEMS)-based motioncontrol device, comprising: generating a velocity profile for eachX-seek; and managing a stiffness of said scanner.
 34. The method ofclaim 33, wherein the velocity profile extends beyond zero as a terminalvelocity, and imparts a reverse velocity equal to that of a desired scanrate, and continues to maintain the scan rate until an end of a track isreached.
 35. The method of claim 34, wherein at the end of a track,performing a turn-around, said performing comprising a step moveperformed by a Y-position servo, while an X-scan servo produces a samescan rate in an opposite direction.
 36. The method of claim 34, whereina step change in a controller output equal to the equilibrium value isgenerated, and wherein a velocity estimator is activated by thecontroller output in addition to a velocity servo output whichsubstantially follows a reference velocity profile.
 37. The system ofclaim 1, wherein said motion comprises two-dimensional motion.